Logistic regression - overview

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In the population, the relationship between the independent variables and the log odds $\ln (\frac{\pi_{y=1}}{1 - \pi_{y=1}})$ is linear

The residuals are independent of one another

Often ignored additional assumption:

Variables are measured without error

Also pay attention to:

Multicollinearity

Outliers

Within each population, the scores on the dependent variable are normally distributed

Group 1 sample is a simple random sample (SRS) from population 1, group 2 sample is an independent SRS from population 2. That is, within and between groups, observations are independent of one another

Test statistic

Test statistic

Model chi-squared test for the complete regression model:

$X^2 = D_{null} - D_K = \mbox{null deviance} - \mbox{model deviance} $
$D_{null}$, the null deviance, is conceptually similar to the total variance of the dependent variable in OLS regression analysis. $D_K$, the model deviance, is conceptually similar to the residual variance in OLS regression analysis.

Wald test for individual $\beta_k$:
The wald statistic can be defined in two ways:

Wald $ = \dfrac{b_k^2}{SE^2_{b_k}}$

Wald $ = \dfrac{b_k}{SE_{b_k}}$

SPSS uses the first definition

Likelihood ratio chi-squared test for individual $\beta_k$:

$X^2 = D_{K-1} - D_K$
$D_{K-1}$ is the model deviance, where independent variable $k$ is excluded from the model. $D_{K}$ is the model deviance, where independent variable $k$ is included in the model.

$t = \dfrac{(\bar{y}_1 - \bar{y}_2) - 0}{\sqrt{\dfrac{s^2_1}{n_1} + \dfrac{s^2_2}{n_2}}} = \dfrac{\bar{y}_1 - \bar{y}_2}{\sqrt{\dfrac{s^2_1}{n_1} + \dfrac{s^2_2}{n_2}}}$
$\bar{y}_1$ is the sample mean in group 1, $\bar{y}_2$ is the sample mean in group 2,
$s^2_1$ is the sample variance in group 1, $s^2_2$ is the sample variance in group 2,
$n_1$ is the sample size of group 1, $n_2$ is the sample size of group 2. The 0 represents the difference in population means according to the null hypothesis.

If you also have code (dummy) variables as independent variables, you can put these in the box below Covariates as well

Instead of transforming your categorical independent variable(s) into code variables, you can also put the untransformed categorical independent variables in the box below Factors. Jamovi will then make the code variables for you 'behind the scenes'